Depends on the game and how much the developer wants to tell a story. For me personally with my bad attention span when reading I focus on single player experiences plus with how interactive it is the story can be more personal.

Yes, I believe that video game is getting better and better at telling stories. The advantage it has over other media forms is the liberty on how to tell you the story and making you a part of the story. Maybe you playing it, Cutscene, text, or the player creating it by himself via choices.